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Separating Earthwork Quantities by Material Depth

Separating Earthwork Quantities by Material Depth

A good friend in Sweden recently suggested we consider trying to solve the following problem which was vexing him at the time:

“In the Nordics there is a demand for separating areas and volumes if the rock cut depth is less or greater than e.g. 1 m. Normally the contractors are being paid by area if rock cut depth is less than 1 m. and by volume if greater than 1 m. Note that it is not the volume below 1 m. that is needed, it is all the volume in the area where rock cut is below 1 m.”

He further distilled the problem as follows:

Given an existing ground surface (EG), a rock surface (Rock), and a finished ground surface (FG), the following quantities would be of interest:

  • Ground cut volume and area: FG below EG but above Rock
  • Rock cut volume and area < 1 m. depth: FG less than 1 m. below Rock
  • Rock cut volume and area > 1 m. depth: FG greater than 1 m. below Rock

Before we begin to look at the solution, a few quick notes:

Let’s start by looking at a picture:

Cross sectional diagram showing relationship of surfaces and materials

Working in imperial units and using 5′ as our cut-off datum, if we offset the Rock surface by -5′ vertically, we can precisely define the region of space that is at a depth of 5′ below Rock. Let’s call this surface Rock-5. Now, wherever the surfaces Rock and Rock-5 intersect FG are points of interest (shown in the picture as vertical lines), since they indicate where the depth of material below Rock starts to increase beyond 5′ or reduce to less than 5′, and also where Rock itself starts to go below or rise above FG. Marking off areas between pairs of such points, we can easily isolate the regions where Rock is less than 5′ above FG. All the remaining regions where Rock is above FG are regions where the depth of material is more than 5′. Note that we’re not interested, here, in regions where Rock is below FG.

Now let’s see how we can use Terra Power Tools to get the correct volumes and areas of the materials that are pertinent to our problem:

3d view of surfaces

  1. We start off by creating the vertical offset surface, Rock-5, using the Create Vertical Offset Surface command, renaming the created surface Rock-5:

Offset ROCK surface

  1. Next, we use the very handy command, Create Split Surfaces, to split the surface FG into three different surfaces using Rock-5 as the splitting surface. These surfaces represent the regions of FG that are above, below, and outside the 2D bounds of Rock-5. The reason for doing this will be become apparent shortly.

Split FG surface aganist ROCK-5 surface

As shown below, the blue surface represents portions of FG that are above Rock-5 and the brown surface represents portions of FG below Rock-5. The portion of FG that is outside the 2D bounds of Rock-5, FG_Outside_Rock-5, is not pertinent to our problem.

Surfaces in 3D and Section

  1. We can now formulate our material definitions based on the following observations:
    1. We’re only interested in material that’s above FG.
    2. Anything above FG, but below Rock is Rock Cut material.
    3. Rock Cut material comes in two varieties:
      1. material that is above the surface FG_Above_Rock-5 (the blue line), and
      2. material that is above the surface FG_Below_Rock-5 (the brown line)
    4. Ground Cut is all material below EG, but above Rock (and of course above FG as well)

We can now define our material table as follows:

Material Table

Computing materials using the above definitions produces the following results:

Cross section showing materials

Volume computation results

Materials displayed in 3d as solids


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